BART trains are running again, but only after transit district officials raised their financial offer by about 48 percent in the final hours of negotiations.

For months BART leaders had correctly insisted they needed to demonstrate fiscal discipline. But, suddenly, all that was abandoned.

The net increase for workers jumped from about 8.0 percent in the district's offer before the four-day strike to 11.7 percent in the final deal, reached Monday. That accounts for increased salary, offset by the greater employee contributions to pensions and health care.

BART officials are remaining mum about the details of the deal until workers hold their ratification votes. When they decide to talk, officials will certainly tout, and quantify, offsetting savings from essential changes to work rules and retiree health care that they won as part of the package.

But they had been seeking those changes all along, and, even there, they settled for less than they wanted. Moreover, even if BART officials had gotten everything they sought, the bigger question is: At what price? Why must the public pay so much for basic efficiencies that are standard in the private sector?

Going into the final weekend, the district had been offering salary increases, some of which employees would use to start making contributions to their pensions. The unions wanted those salary increases and reimbursement for the pension contributions. In the end, they got it.

BART was already paying some of the best public transit wages in the nation. On top of that, workers made no contributions to their pensions and paid only $92 a month toward their health care -- regardless of the number of dependents.

Meanwhile, BART faces billions of dollars of capital needs. Directors know they need to preserve funds to help pay that bill, and they need to demonstrate financial restraint to persuade voters to approve needed future tax increases.

They just made that job more difficult. To understand how much BART gave up sealing the deal, let's look at key components:

Salary: BART officials and, consequently, news accounts consistently understated the amount of the salary increases the district was offering. For example, when Gov. Jerry Brown imposed the 60-day cooling off period in August, the district was offering a four-year contract with 2 percent raises in each of the first two years and 2.5 percent raises in the last two years.

BART consistently portrayed this as a 9 percent increase over four years. That ignored the effect of compounding: Each increase would be applied to the salary from the previous year. In fact, the offer then was 9.3 percent.

Similarly, going into last weekend, the district portrayed its so-called "last, best and final" offer of 3 percent each year as a 12 percent deal when it was actually about 12.6 percent. And when the bargaining was over, they had agreed to 16.3 percent compounded.

Pensions: BART officials wanted workers to start sharing the cost of their pensions. At the beginning of August, the district was seeking a contribution of 2 percent of salary the first year, ratcheting up to 5 percent by the fourth year of the contract. But later that month, they reduced that to 1 percent the first year, increasing to 4 percent the last.

Workers walk the picket line at the Lake Merritt BART station in Oakland, Calif., on Monday, Oct. 21, 2013. (Kristopher Skinner/Bay Area News Group)

Health care: The district also wanted employees to pay more toward health benefits. In the end they settled on a flat increase of $40 a month, which averages about 0.6 percent of salary.

In summary: Take the 16.3 percent salary increase over four years and subtract employee pension contributions, 4 percent by the fourth year, and the higher health care contribution, 0.6 percent. The net: 11.7 percent.

Those numbers do not account for the extra benefit costs associated with the salary increases. Every dollar of salary requires that the district make greater contributions to benefits such as workers' compensation insurance and, ironically, pensions. As a result, the full cost to the district was significantly more.

That said, the base salary and benefit numbers provide insight into how desperately district officials wanted to settle the strike.